Physical origin of Davydov splitting and resonant Raman spectroscopy of Davydov components in multilayer MoTe 2

We systematically study the high-resolution and polarized Raman spectra of multilayer (ML) ${\mathrm{MoTe}}_{2}$. The layer-breathing (LB) and shear (C) modes are observed in the ultralow-frequency region, which are used to quantitatively evaluate the interlayer coupling in ML ${\mathrm{MoTe}}_{2}$ based on the linear chain model, in which only the nearest interlayer coupling is considered. The Raman spectra on three different substrates verify the negligible substrate effect on the phonon frequencies of ML ${\mathrm{MoTe}}_{2}$. Ten excitation energies are used to measure the high-frequency modes of $N$-layer ${\mathrm{MoTe}}_{2}$ ($N\mathrm{L} {\mathrm{MoTe}}_{2}$; $N$ is an integer). Under the resonant excitation condition, we observe $N$\char21{}dependent Davydov components in ML ${\mathrm{MoTe}}_{2}$, originating from the Raman-active ${A}_{1}^{\ensuremath{'}}({A}_{1g}^{2})$ modes at \ensuremath{\sim}$172\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$. More than two Davydov components are observed in $N\mathrm{L} {\mathrm{MoTe}}_{2}$ for $Ng4$ by Raman spectroscopy. The $N$-dependent Davydov components are further investigated based on the symmetry analysis. A van der Waals model only considering the nearest interlayer coupling has been proposed to well understand the Davydov splitting of high-frequency ${A}_{1}^{\ensuremath{'}}({A}_{1g}^{2})$ modes. The different resonant profiles for the two Davydov components in 3L ${\mathrm{MoTe}}_{2}$ indicate that proper excitation energy of $\ensuremath{\sim}1.8\ensuremath{-}2.2$ eV must be chosen to observe the Davydov splitting in ML ${\mathrm{MoTe}}_{2}$. Our work presents a simple way to identify layer number of ultrathin ${\mathrm{MoTe}}_{2}$ flakes by the corresponding number and peak position of Davydov components. Our work also provides a direct evidence from Raman spectroscopy of how the nearest van der Waals interactions significantly affect the frequency of the high-frequency intralayer phonon modes in multilayer ${\mathrm{MoTe}}_{2}$ and expands the understanding on the lattice vibrations and interlayer coupling of transition metal dichalcogenides and other two-dimensional materials.